About

Chaos Theory

Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part. There were still many facets of the universe that were an enigma to physicists. Mathematicians could indeed illustrate patterns in nature but there were many aspects of Mother Nature that remained a mystery to Physicists and Mathematicians alike. Mathematics is an integral part of physics. It provides an order and a guide to thinking; it shows the relationship between many physical phenomenons. The error in mathematics until that point was linearity. "Clouds are not spheres, mountains are not cones, bark is not smooth, nor does lightning travel in a straight line." - Benoit Mandlebrot. Was it not beyond reason that a process, which is dictated by that regularity, could master a world that shows almost no predictability whatsoever? A new science and a new kind of mathematics were developed that could show the universe's idiosyncrasies. This new amalgam of mathematics and physics takes the order of linearity and shows how it relates to the unpredictability of the world around us. It is called Chaos Theory.

The secular definition of chaos can be misleading when the word is used in a scientific context. As defined by Webster's dictionary chaos is total disorder. That may lead one to believe that chaos theory is indeed the study of total disorder, which it truly is not. In 1986 at a prestigious conference on Chaos another definition for chaos was introduced. It is stochastic behavior occurring in a deterministic set. This definition of chaos was hesitantly brought forth. The scientists, mathematicians and intellectuals present were hesitant to define a concept they did not truly understand yet. They left the scientific community with a rather cryptic and oxymoronic definition of chaos. Deterministic sets behave by precise unbreakable law. Stochastic behavior is the opposite of deterministic it has no finite laws, it is totally dependent upon chance. The dissected definition of chaos is lawless behavior that is ruled entirely by law. (Stewart 16-17)

The principles of Chaos Theory are complex and abstract. Perhaps the simplest and most essential ideas behind chaos theory are embodied in the aphorism known as the Butterfly Effect. The butterfly effect states that the flapping of a butterfly's wings in Hong Kong can change the weather in New York. It means that a minuscule change in the initial conditions of a system, in this case the weather, is magnified greatly in the end conditions of that same system. The ultra sensitivity to the initial conditions of a system was not a new and striking discovery. In fact it was shown in ancient folklore;

"For want of a nail, the shoe was lost; For want of a shoe, the horse was lost; For want of a horse, the rider was lost; For want of a rider, the battle was lost; For the want of a battle, the kingdom was lost!"

The smallest variation in the initial conditions of a system can result in huge differences in concluding events. There was no nail, and because of this seemingly insignificant detail in the initial condition, the kingdom was lost. Another example of the butterfly affect is two pieces of wood floating on a river. Place those two logs at nearly the same point on the river and let them go. It is absolutely impossible to predict where those logs will be later downstream. When those logs are set on the water a slight breeze, a fish that swims underneath one of them, or even a single droplet of additional water in the initial stage can totally change the end result until no...

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sequence had changed differently. The pattern had diverged, ending up being extremely different.
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...around us. This thinking is known as ChaosTheory.
Although the word "chaos" is traditionally associated with total disorder, it is misleading when describing ChaosTheory. In 1986, a group of scientists submitted a new definition for chaos: "Stochastic behavior occurring in a deterministic set." This definition was later changed to "Lawless behavior that is ruled by law."
Although ChaosTheory has only been around for about 50 years, its principles have been around for much longer than that. It wasn't until recently that scientific knowledge progressed to the point where the distinction between linear and chaotic science began to become apparent. In 1898, a French mathematician named Jacques Hadamard published a study describing the chaotic motion of free particles gliding on a negative curvature. Hadamard was able to show that their trajectories were unstable and unpredictable, diverging exponentially from one another. In the early 1900s, Henri Poincare, the great French mathematician/philosopher/physicist, declared the existence of non-periodic orbits. Both of these discoveries would play a major role in the formation of ChaosTheory 60 years later. As scientific and technological knowledge began to expand dramatically in the mid-1900s, it became more and more apparent that linear science could not explain certain...

...﻿The Butterfly Theory in our Lives
It has been said that something as small as the flutter of a butterfly's wing can ultimately cause a typhoon halfway around the world.
The butterfly effect is a tenant to the Chaostheory. Chaos can be described as disorientated or random behavior based on initial circumstances. In scientific jargon the term “chaos” does not carry a negative connotation, instead the unpredictable behavior that it relates with is desirable. The ChaosTheory is a mathematical sub-discipline that studies complex systems, Such as the earth's weather systems or the migratory patterns of birds.
Chaos is everywhere, from nature's most intimate considerations to an art form of any kind. The Chaostheory defines large complex systems, namely systems that are in such varying and constant motion that computers are required to calculate the varying possibilities for their outcomes. The butterfly effect simply describes how small unrelated behavior based on initial conditions can ultimately affect large these complex systems.
The concept of the butterfly effect is attributed to Edward Norton Lorenz, a mathematician and meteorologist. Lorenz was running global climate models on his computer one day and, hoping to save himself some time, ran one model from the middle rather than the beginning. The two weather...

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ChaosTheory Alba 10
Chaostheory is a complicated field of study that combines mathematics, physics, biology, and philosophy. It focuses on dynamic, non-linear systems that are very sensitive to small changes. This is also known as the butterfly effect. It is also something that I believe that I witness every day as a student driving to school.
Essentially, the butterfly effect states that a small action can have profound effects on seemingly unrelated events later on. The scientist Edward Lorenz coined the term in 1972 when studying weather patterns. He wondered if butterfly flapping its wings could somehow affect tornado winds. Lorenz never proved definitively whether a butterfly flapping its wings in Brazil actually caused a storm in Texas. However, he did conclude that small changes in weather could create dramatic turbulence that made it impossible to accurately predict weather beyond a few weeks or even a few days.
While it is easy for a non-scientist like myself to get confused by the complex details, the butterfly effect has been explained in simple terms in pop culture. In fact, this is where I learned most of the details about chaostheory and the butterfly effect. The most famous examples occur in science fiction examples related to time travel. Ray Bradbury wrote a short story called “The Sound of Thunder” in 1952 where a group of people travels...

...﻿ChaosTheoryChaostheory as a name comes from the fact that the systems the theory describes (non-linear systems) would seem to be disordered or random or at least unpredictable. Chaostheory tries to find some underlying order in what appears to be random events or data.
Edward Lorenz was an early pioneer of the theory. He was working on weather predictions in 1961 and was using a computer to help with the calculations. Lorenz had initiated a sequence of data based on twelve variables in his attempt to predict weather. He wanted to see the sequence again, so re-entered the data. To save time, he began the new simulation in the middle of the old, using a printout from the prior calculations. The weather patterns the computer predicted from the new simulation was very different from what had been initially predicted. Working backward, Lorenz discovered that he had entered the data only out to the third decimal point, whereas in the initial simulation, he had used the same data out to the fifth decimal point. These differences, although very small, should have had only a tiny impact, if any, on the resultant predictions, but the opposite was true -- the impact was huge.
Chaotic systems are unstable. Two sets of nearly the same initial conditions will end up with two very separate final conditions. For example, if identical twin girls that had been raised...

...Explaining ChaosTheory is not easy. I am merely going to focus to get closer to it and try explaining in my paper the basics of so called ’ChaosTheory’. To do that in financial sence,of course, it might be the best way to try analysing from macro stand point looking at world as a hole, looking at the big picture. Science is trying to explain chaos as long as it exists and try to extrapolate the formula for it, trying to get the predictions as accurate as possible.
Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part. There were still many facets of the universe that were an enigma to physicists. Mathematicians could indeed illustrate patterns in nature but there were many aspects of Mother Nature that remained a mystery to Physicists and Mathematicians alike. Mathematics is an integral part of physics. It provides an order and a guide to thinking; it shows the relationship between many physical phenomenons. The error in mathematics until that point was linearity....

...of chaostheory in Tom Stoppard’s major play, Arcadia. Although chaos and chaotic systems mainly belong to the sciences of physics and mathematics, the theory of chaos as a postmodern matrix can be discussed in both art and literature. Stoppard’s, and other interdisciplinary author’s, main source is James Gleick famous book “Chaos: Making a New Science”. Chaostheory is a branch of nonlinear dynamics that have an orderly disordered nature; i.e. it shows turbulence in any small scale, however its orderly pattern appears in a large scale. Chaostheory is the main essence of most of Stoppard’s plays, in that they seek to find out the hidden order behind chaos. Stoppard, as an artist, tries to understand and convey the real identity of the human being. He accompanies this very theme with the conceptions such as entropy and the second law of thermodynamics, history, love and irreversibility of time in two historical periods. Stoppard makes use of the internal paradox of this theory as a rich metaphor, and as a trajectory for his characters to gain knowledge. The play is considered as a site for growing two kinds of knowledge: scientific knowledge versus emotional knowledge. Gaining each kind of knowledge depends on whether the subject character possesses the classical tendencies or romantic nature, however in the...

...Chaos in Jurassic Park
"Chaostheory proves that unpredictability is built into our daily lives."(Crichton 313). Ian Malcolm's words resolve the book, Jurassic Park, in a very absolute way. Throughout the book, Malcolm, spoke about chaostheory and his self proclaimed "Malcolm Effect" to explain his reasoning in his predictions. Ian Malcolm had predicted the demise of Jurassic Park even before its opening, as well as its multiple problems and difficulties. Malcolm's theory is evidenced countless times throughout the story of Jurassic Park; dinosaurs are breeding, dinosaurs are escaping, and systems fail.
"They're breeding."(Crichton 164). Ian Malcolm had predicted that the dinosaurs of Jurassic Park were, in fact, breeding. This was discovered to be true later on in the book, when the numbers of dinosaurs were exceeding the expected count. The use of frog DNA to restore missing portions of dinosaur DNA was the underlying cause. It gave them the ability to reproduce by switching gender. Malcolm had said, "But life finds a way"(Crichton 160), early on in the trip to Jurassic Park, and as he had said, life truly did find a way. The very process of making certain that the dinosaurs were all female, thus unable to reproduce, through first, genetically engineering them to be female, and then irradiating them may have been the very reason why they did in fact reproduce. Any...